Sam opened a savings account with $400. He earns $1,640 a month at his job and will deposit 3% of his monthly pay every month into his new savings account. Assuming he doesn't withdraw money from his savings account, which equation shows the balance \$y\$ of his savings account \$x\$ months after he opened it?
A. $y=0.03 x+400$
B. $y=12 x+400$
C. $y=400 x+1640$
D. $y=49.2 x+400
Answer (1)
Calculate the monthly deposit: 3% of $1 , 640 is $49.2 .
Formulate the equation: The balance y after x months is the initial deposit plus the monthly deposit times the number of months.
Write the equation: y = 400 + 49.2 x .
The equation representing the balance is y = 49.2 x + 400 .
Explanation
Understanding the Problem Let's analyze the problem. Sam starts with an initial deposit of $400 in his savings account. He earns $1 , 640 per month and deposits 3% of his monthly pay into the account. We need to find an equation that represents the balance y of his savings account after x months, assuming he makes no withdrawals.
Calculating Monthly Deposit First, we need to calculate how much Sam deposits each month. This is 3% of his monthly income of $1 , 640 . To find this amount, we multiply 1 , 640 by 0.03 .
Determining the Monthly Deposit Amount The monthly deposit is 0.03 × 1640 = 49.2 . So, Sam deposits $49.2 each month.
Formulating the Equation Now, we can write the equation for the balance y of the savings account after x months. The balance will be the initial deposit plus the monthly deposit times the number of months. The initial deposit is $400 , and the monthly deposit is $49.2 . Therefore, the equation is: y = 400 + 49.2 x , which can also be written as y = 49.2 x + 400 .
Final Answer The equation that shows the balance y of his savings account x months after he opened it is y = 49.2 x + 400 .
Examples
Imagine you are saving up for a new bicycle that costs $700 . You start with $400 in your savings account and deposit 3% of your $1 , 640 monthly income into the account. Using the equation y = 49.2 x + 400 , you can calculate how many months it will take to save enough money to buy the bicycle. This equation helps you track your savings progress and plan your finances effectively.
